Seiberg-Witten theory, matrix model and AGT relation

TL;DR

This paper explores a Penner-type matrix model that explains the AGT relation, derives spectral curves matching M-theory, and computes free energies that reproduce Seiberg-Witten theory amplitudes.

Contribution

It explicitly evaluates free energies of new matrix models for Seiberg-Witten theories with flavors, confirming their correspondence with known amplitudes.

Findings

Spectral curves match those from M-theory.

Free energies reproduce Seiberg-Witten amplitudes.

New matrix models describe theories with N_f=2,3 flavors.

Abstract

We discuss the Penner-type matrix model which has been proposed to explain the AGT relation between the 2-dimensional Liouville theory and 4-dimensional N=2 superconformal gauge theories. In our previous communication we have obtained the spectral curve of the matrix model and showed that it agrees with that derived from M-theory. We have also discussed the decoupling limit of massive flavors and proposed new matrix models which describe Seiberg-Witten theory with flavors N_f=2,3. In this article we explicitly evaluate the free energy of these matrix models and show that they in fact reproduce the amplitudes of Seiberg-Witten theory.